Eigenvalue problems for the p-Laplacian

• Published in: Nonlinear analysis Vol. 64; no. 5; pp. 1057 - 1099
• Main Author: LE, An
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2006; Elsevier
• Subjects: Exact sciences and technology; Ljusternik–Schnirelman principle; Mathematical analysis; Mathematics; Nonlinear eigenvalue problems; p-Laplacian; Partial differential equations; Sciences and techniques of general use; Variational methods; p-Laplacian; Variational methods; 35J60; Nonlinear eigenvalue problems; 35B45; 35J70; Ljusternik–Schnirelman principle; P laplacian; Nonlinear analysis; 35J70 Nonlinear eigenvalue problems; Nonlinear problems; Eigenvalue problem; Ljusternik Schnirelman principle; Ljusternik-Schnirelman principle

We study nonlinear eigenvalue problems for the p -Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of...